Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

[EN] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a ¿smooth + singular¿ decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.Stephane Bordas would like to thank the partial financial support of the Royal Academy of Engineering and of the Leverhulme Trust for his Senior Research Fellowship Towards the next generation surgical simulators as well as the financial support for Octavio A. Gonzalez-Estrada and Stephane Bordas from the UK Engineering Physical Science Research Council (EPSRC) under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method. Stephane Bordas also thanks partial financial support of the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) and the FP7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology, INSIST". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support from Universitat Politecnica de Valencia, PROMETEO/2012/023 and Generalitat Valenciana are also acknowledged.González Estrada, OA.; Natarajan, S.; J.J. Ródenas; Nguyen-Xuan, H.; Bordas, S. (2013). Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics. 52(1):37-52. https://doi.org/10.1007/s00466-012-0795-6S3752521Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. 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Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Chaste: an open source C++ library for computational physiology and biology

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to "re-invent the wheel" with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials

Macrocheles species (Acari: Macrochelidae) associated with human corpses in Europe

The biology of macrochelid mites might offer new venues for the interpretation of the environmental conditions surrounding human death and decomposition. Three human corpses, one from Sweden and two from Spain, have been analysed for the occurrence of Macrochelidae species. Macrocheles muscaedomesticae females were associated with a corpse that was found in a popular beach area of southeast Spain. Their arrival coincides with the occurrence of one of their major carrier species, the filth fly Fannia scalaris, the activity of which peaks during mid-summer. M. glaber specimens were collected from a corpse in a shallow grave in a forest in Sweden at the end of summer, concurrent with the arrival of beetles attracted by odours from the corpse. M. perglaber adults were sampled from a corpse found indoors in the rural surroundings of Granada city, Spain. The phoretic behaviour of this species is similar to that of M. glaber, but being more specific to Scarabaeidae and Geotrupidae dung beetles, most of which favour human faeces. M. muscaedomesticae is known from urban and rural areas and poultry farms; M. glaber from outdoors, particularly the countryside; while M. perglaber from outdoor, rural, and remote, potentially mountainous locations. M. muscaedomesticae and M. perglaber are reported for the first time from the Iberian Peninsula. This is the first record of M. perglaber from human remains

Macrocheles species (Acari: Macrochelidae) associated with human corpses in Europe

The biology of macrochelid mites might offer new venues for the interpretation of the environmental conditions surrounding human death and decomposition. Three human corpses, one from Sweden and two from Spain, have been analysed for the occurrence of Macrochelidae species. Macrocheles muscaedomesticae females were associated with a corpse that was found in a popular beach area of southeast Spain. Their arrival coincides with the occurrence of one of their major carrier species, the filth fly Fannia scalaris, the activity of which peaks during mid-summer. M. glaber specimens were collected from a corpse in a shallow grave in a forest in Sweden at the end of summer, concurrent with the arrival of beetles attracted by odours from the corpse. M. perglaber adults were sampled from a corpse found indoors in the rural surroundings of Granada city, Spain. The phoretic behaviour of this species is similar to that of M. glaber, but being more specific to Scarabaeidae and Geotrupidae dung beetles, most of which favour human faeces. M. muscaedomesticae is known from urban and rural areas and poultry farms; M. glaber from outdoors, particularly the countryside; while M. perglaber from outdoor, rural, and remote, potentially mountainous locations. M. muscaedomesticae and M. perglaber are reported for the first time from the Iberian Peninsula. This is the first record of M. perglaber from human remains

Seasonal variations in pore water and sediment geochemistry of littoral lake sediments (Asylum Lake, MI, USA)

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Multi-messenger observations of a binary neutron star merger

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Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic centre

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